Predict best price using neural network?
This is possible.... but there's no reason to use a neural network! Your best bet on a problem like this is likely to use a logistical regression for the yes/no aspect of the question and a linear regression (or combination of linear regressions) to answer the pricing question - there are also ways of simply using linear regressions and setting up cutoffs to answer the yes/no question.

The reality is that the accuracy of such a model/series of models would depend entirely on the quality and quantity of the data, but it's unlikely that in this case a neural network would provide a better result than smart usage of simpler models.